LMFDB - Embedded newform 197.4.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(1,197)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$11.6233762711$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-3.25705 q^{2} -0.297531 q^{3} +2.60839 q^{4} -8.26136 q^{5} +0.969073 q^{6} +15.5528 q^{7} +17.5608 q^{8} -26.9115 q^{9} +26.9077 q^{10} +24.4046 q^{11} -0.776075 q^{12} +44.1406 q^{13} -50.6562 q^{14} +2.45801 q^{15} -78.0634 q^{16} -0.107242 q^{17} +87.6521 q^{18} -94.4553 q^{19} -21.5488 q^{20} -4.62743 q^{21} -79.4870 q^{22} +144.904 q^{23} -5.22487 q^{24} -56.7499 q^{25} -143.768 q^{26} +16.0403 q^{27} +40.5676 q^{28} +24.1713 q^{29} -8.00587 q^{30} -259.045 q^{31} +113.770 q^{32} -7.26112 q^{33} +0.349293 q^{34} -128.487 q^{35} -70.1955 q^{36} -412.288 q^{37} +307.646 q^{38} -13.1332 q^{39} -145.076 q^{40} -362.243 q^{41} +15.0718 q^{42} +239.777 q^{43} +63.6566 q^{44} +222.325 q^{45} -471.959 q^{46} -62.5601 q^{47} +23.2263 q^{48} -101.111 q^{49} +184.837 q^{50} +0.0319078 q^{51} +115.136 q^{52} -518.071 q^{53} -52.2442 q^{54} -201.615 q^{55} +273.119 q^{56} +28.1034 q^{57} -78.7271 q^{58} -292.939 q^{59} +6.41144 q^{60} -535.519 q^{61} +843.724 q^{62} -418.548 q^{63} +253.951 q^{64} -364.661 q^{65} +23.6498 q^{66} +566.243 q^{67} -0.279729 q^{68} -43.1133 q^{69} +418.489 q^{70} +413.907 q^{71} -472.586 q^{72} -336.802 q^{73} +1342.84 q^{74} +16.8848 q^{75} -246.376 q^{76} +379.559 q^{77} +42.7754 q^{78} +492.451 q^{79} +644.910 q^{80} +721.837 q^{81} +1179.85 q^{82} +1180.14 q^{83} -12.0701 q^{84} +0.885966 q^{85} -780.967 q^{86} -7.19170 q^{87} +428.563 q^{88} +663.513 q^{89} -724.125 q^{90} +686.508 q^{91} +377.964 q^{92} +77.0740 q^{93} +203.762 q^{94} +780.330 q^{95} -33.8502 q^{96} -336.952 q^{97} +329.324 q^{98} -656.764 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) $ 22 * q - 6 * q^2 - 34 * q^3 + 68 * q^4 - 31 * q^5 - 24 * q^6 - 102 * q^7 - 93 * q^8 + 152 * q^9 - 133 * q^10 - 100 * q^11 - 272 * q^12 - 223 * q^13 - 55 * q^14 - 166 * q^15 + 112 * q^16 - 114 * q^17 - 389 * q^18 - 529 * q^19 - 441 * q^20 - 148 * q^21 - 671 * q^22 - 208 * q^23 - 555 * q^24 + 35 * q^25 - 408 * q^26 - 994 * q^27 - 1202 * q^28 - 2 * q^29 - 365 * q^30 - 1261 * q^31 - 1020 * q^32 - 790 * q^33 - 814 * q^34 - 968 * q^35 + 94 * q^36 - 792 * q^37 - 184 * q^38 - 368 * q^39 - 1914 * q^40 - 271 * q^41 - 1157 * q^42 - 1349 * q^43 - 998 * q^44 - 1533 * q^45 - 1371 * q^46 - 986 * q^47 - 1966 * q^48 - 40 * q^49 + 1631 * q^50 - 36 * q^51 - 1382 * q^52 + 248 * q^53 + 2903 * q^54 - 566 * q^55 + 4800 * q^56 + 914 * q^57 + 351 * q^58 - 1281 * q^59 + 5149 * q^60 + 510 * q^61 + 2237 * q^62 + 120 * q^63 + 3185 * q^64 + 2558 * q^65 + 8308 * q^66 - 3070 * q^67 + 4625 * q^68 + 302 * q^69 + 2087 * q^70 + 101 * q^71 + 4511 * q^72 - 3352 * q^73 + 4501 * q^74 - 752 * q^75 - 334 * q^76 - 492 * q^77 + 7825 * q^78 - 1313 * q^79 + 3098 * q^80 + 2078 * q^81 - 1243 * q^82 - 2631 * q^83 + 7518 * q^84 + 84 * q^85 + 7448 * q^86 - 1046 * q^87 - 3285 * q^88 + 798 * q^89 + 6009 * q^90 - 3992 * q^91 + 5966 * q^92 + 1978 * q^93 + 3517 * q^94 + 284 * q^95 + 10181 * q^96 - 3693 * q^97 + 2932 * q^98 - 502 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−3.25705	−1.15154	−0.575771	−	0.817611i	$-0.695298\pi$
$2$	−3.25705	−1.15154	−0.575771	+	0.817611i	$0.695298\pi$
$3$	−0.297531	−0.0572598	−0.0286299	−	0.999590i	$-0.509114\pi$
$3$	−0.297531	−0.0572598	−0.0286299	+	0.999590i	$0.509114\pi$
$4$	2.60839	0.326048
$5$	−8.26136	−0.738919	−0.369459	−	0.929247i	$-0.620457\pi$
$5$	−8.26136	−0.738919	−0.369459	+	0.929247i	$0.620457\pi$
$6$	0.969073	0.0659371
$7$	15.5528	0.839771	0.419885	−	0.907577i	$-0.362070\pi$
$7$	15.5528	0.839771	0.419885	+	0.907577i	$0.362070\pi$
$8$	17.5608	0.776084
$9$	−26.9115	−0.996721
$10$	26.9077	0.850896
$11$	24.4046	0.668933	0.334466	−	0.942408i	$-0.391444\pi$
$11$	24.4046	0.668933	0.334466	+	0.942408i	$0.391444\pi$
$12$	−0.776075	−0.0186695
$13$	44.1406	0.941722	0.470861	−	0.882207i	$-0.343943\pi$
$13$	44.1406	0.941722	0.470861	+	0.882207i	$0.343943\pi$
$14$	−50.6562	−0.967031
$15$	2.45801	0.0423104
$16$	−78.0634	−1.21974
$17$	−0.107242	−0.00153000	−0.000765001	−	1.00000i	$-0.500244\pi$
$17$	−0.107242	−0.00153000	−0.000765001		1.00000i	$0.500244\pi$
$18$	87.6521	1.14777
$19$	−94.4553	−1.14050	−0.570251	−	0.821470i	$-0.693154\pi$
$19$	−94.4553	−1.14050	−0.570251	+	0.821470i	$0.693154\pi$
$20$	−21.5488	−0.240923
$21$	−4.62743	−0.0480852
$22$	−79.4870	−0.770304
$23$	144.904	1.31367	0.656837	−	0.754033i	$-0.271894\pi$
$23$	144.904	1.31367	0.656837	+	0.754033i	$0.271894\pi$
$24$	−5.22487	−0.0444384
$25$	−56.7499	−0.453999
$26$	−143.768	−1.08443
$27$	16.0403	0.114332
$28$	40.5676	0.273806
$29$	24.1713	0.154776	0.0773878	−	0.997001i	$-0.475342\pi$
$29$	24.1713	0.154776	0.0773878	+	0.997001i	$0.475342\pi$
$30$	−8.00587	−0.0487221
$31$	−259.045	−1.50084	−0.750418	−	0.660963i	$-0.770148\pi$
$31$	−259.045	−1.50084	−0.750418	+	0.660963i	$0.770148\pi$
$32$	113.770	0.628499
$33$	−7.26112	−0.0383030
$34$	0.349293	0.00176186
$35$	−128.487	−0.620522
$36$	−70.1955	−0.324979
$37$	−412.288	−1.83188	−0.915941	−	0.401312i	$-0.868554\pi$
$37$	−412.288	−1.83188	−0.915941	+	0.401312i	$0.868554\pi$
$38$	307.646	1.31334
$39$	−13.1332	−0.0539229
$40$	−145.076	−0.573463
$41$	−362.243	−1.37983	−0.689914	−	0.723892i	$-0.742351\pi$
$41$	−362.243	−1.37983	−0.689914	+	0.723892i	$0.742351\pi$
$42$	15.0718	0.0553721
$43$	239.777	0.850365	0.425182	−	0.905108i	$-0.360210\pi$
$43$	239.777	0.850365	0.425182	+	0.905108i	$0.360210\pi$
$44$	63.6566	0.218104
$45$	222.325	0.736496
$46$	−471.959	−1.51275
$47$	−62.5601	−0.194156	−0.0970780	−	0.995277i	$-0.530950\pi$
$47$	−62.5601	−0.194156	−0.0970780	+	0.995277i	$0.530950\pi$
$48$	23.2263	0.0698422
$49$	−101.111	−0.294785
$50$	184.837	0.522799
$51$	0.0319078	8.76076e−5 0
$52$	115.136	0.307047
$53$	−518.071	−1.34269	−0.671345	−	0.741145i	$-0.734283\pi$
$53$	−518.071	−1.34269	−0.671345	+	0.741145i	$0.734283\pi$
$54$	−52.2442	−0.131658
$55$	−201.615	−0.494287
$56$	273.119	0.651732
$57$	28.1034	0.0653050
$58$	−78.7271	−0.178231
$59$	−292.939	−0.646397	−0.323199	−	0.946331i	$-0.604758\pi$
$59$	−292.939	−0.646397	−0.323199	+	0.946331i	$0.604758\pi$
$60$	6.41144	0.0137952
$61$	−535.519	−1.12404	−0.562018	−	0.827125i	$-0.689975\pi$
$61$	−535.519	−1.12404	−0.562018	+	0.827125i	$0.689975\pi$
$62$	843.724	1.72828
$63$	−418.548	−0.837018
$64$	253.951	0.495998
$65$	−364.661	−0.695856
$66$	23.6498	0.0441075
$67$	566.243	1.03250	0.516251	−	0.856438i	$-0.327327\pi$
$67$	566.243	1.03250	0.516251	+	0.856438i	$0.327327\pi$
$68$	−0.279729	−0.000498854 0
$69$	−43.1133	−0.0752207
$70$	418.489	0.714557
$71$	413.907	0.691855	0.345927	−	0.938261i	$-0.387564\pi$
$71$	413.907	0.691855	0.345927	+	0.938261i	$0.387564\pi$
$72$	−472.586	−0.773539
$73$	−336.802	−0.539996	−0.269998	−	0.962861i	$-0.587023\pi$
$73$	−336.802	−0.539996	−0.269998	+	0.962861i	$0.587023\pi$
$74$	1342.84	2.10949
$75$	16.8848	0.0259959
$76$	−246.376	−0.371859
$77$	379.559	0.561750
$78$	42.7754	0.0620944
$79$	492.451	0.701330	0.350665	−	0.936501i	$-0.385956\pi$
$79$	492.451	0.701330	0.350665	+	0.936501i	$0.385956\pi$
$80$	644.910	0.901289
$81$	721.837	0.990175
$82$	1179.85	1.58893
$83$	1180.14	1.56068	0.780342	−	0.625353i	$-0.215045\pi$
$83$	1180.14	1.56068	0.780342	+	0.625353i	$0.215045\pi$
$84$	−12.0701	−0.0156781
$85$	0.885966	0.00113055
$86$	−780.967	−0.979230
$87$	−7.19170	−0.00886243
$88$	428.563	0.519148
$89$	663.513	0.790250	0.395125	−	0.918627i	$-0.370701\pi$
$89$	663.513	0.790250	0.395125	+	0.918627i	$0.370701\pi$
$90$	−724.125	−0.848106
$91$	686.508	0.790831
$92$	377.964	0.428321
$93$	77.0740	0.0859377
$94$	203.762	0.223579
$95$	780.330	0.842738
$96$	−33.8502	−0.0359877
$97$	−336.952	−0.352704	−0.176352	−	0.984327i	$-0.556430\pi$
$97$	−336.952	−0.352704	−0.176352	+	0.984327i	$0.556430\pi$
$98$	329.324	0.339457
$99$	−656.764	−0.666740
$100$	−148.026	−0.148026
$101$	−1753.02	−1.72705	−0.863526	−	0.504304i	$-0.831749\pi$
$101$	−1753.02	−1.72705	−0.863526	+	0.504304i	$0.831749\pi$
$102$	−0.103925	−0.000100884 0
$103$	−1848.63	−1.76846	−0.884229	−	0.467054i	$-0.845315\pi$
$103$	−1848.63	−1.76846	−0.884229	+	0.467054i	$0.845315\pi$
$104$	775.142	0.730855
$105$	38.2289	0.0355310
$106$	1687.38	1.54616
$107$	−553.585	−0.500160	−0.250080	−	0.968225i	$-0.580457\pi$
$107$	−553.585	−0.500160	−0.250080	+	0.968225i	$0.580457\pi$
$108$	41.8394	0.0372777
$109$	−621.460	−0.546102	−0.273051	−	0.962000i	$-0.588033\pi$
$109$	−621.460	−0.546102	−0.273051	+	0.962000i	$0.588033\pi$
$110$	656.671	0.569192
$111$	122.668	0.104893
$112$	−1214.10	−1.02430
$113$	1439.42	1.19832	0.599158	−	0.800631i	$-0.295502\pi$
$113$	1439.42	1.19832	0.599158	+	0.800631i	$0.295502\pi$
$114$	−91.5342	−0.0752014
$115$	−1197.10	−0.970698
$116$	63.0480	0.0504643
$117$	−1187.89	−0.938635
$118$	954.118	0.744353
$119$	−1.66791	−0.00128485
$120$	43.1645	0.0328364
$121$	−735.416	−0.552529
$122$	1744.21	1.29437
$123$	107.779	0.0790087
$124$	−675.690	−0.489345
$125$	1501.50	1.07439
$126$	1363.23	0.963861
$127$	−1650.07	−1.15292	−0.576458	−	0.817127i	$-0.695566\pi$
$127$	−1650.07	−1.15292	−0.576458	+	0.817127i	$0.695566\pi$
$128$	−1737.30	−1.19966
$129$	−71.3411	−0.0486917
$130$	1187.72	0.801307
$131$	386.313	0.257652	0.128826	−	0.991667i	$-0.458879\pi$
$131$	386.313	0.257652	0.128826	+	0.991667i	$0.458879\pi$
$132$	−18.9398	−0.0124886
$133$	−1469.04	−0.957761
$134$	−1844.28	−1.18897
$135$	−132.515	−0.0844820
$136$	−1.88325	−0.00118741
$137$	−827.801	−0.516232	−0.258116	−	0.966114i	$-0.583102\pi$
$137$	−827.801	−0.516232	−0.258116	+	0.966114i	$0.583102\pi$
$138$	140.422	0.0866198
$139$	−612.420	−0.373703	−0.186852	−	0.982388i	$-0.559828\pi$
$139$	−612.420	−0.373703	−0.186852	+	0.982388i	$0.559828\pi$
$140$	−335.144	−0.202320
$141$	18.6136	0.0111173
$142$	−1348.12	−0.796700
$143$	1077.23	0.629949
$144$	2100.80	1.21574
$145$	−199.688	−0.114367
$146$	1096.98	0.621828
$147$	30.0837	0.0168793
$148$	−1075.40	−0.597282
$149$	348.305	0.191505	0.0957527	−	0.995405i	$-0.469474\pi$
$149$	348.305	0.191505	0.0957527	+	0.995405i	$0.469474\pi$
$150$	−54.9948	−0.0299354
$151$	−1645.16	−0.886629	−0.443315	−	0.896366i	$-0.646198\pi$
$151$	−1645.16	−0.886629	−0.443315	+	0.896366i	$0.646198\pi$
$152$	−1658.71	−0.885125
$153$	2.88604	0.00152499
$154$	−1236.24	−0.646879
$155$	2140.07	1.10900
$156$	−34.2564	−0.0175814
$157$	3601.58	1.83081	0.915405	−	0.402534i	$-0.131871\pi$
$157$	3601.58	1.83081	0.915405	+	0.402534i	$0.131871\pi$
$158$	−1603.94	−0.807611
$159$	154.142	0.0768822
$160$	−939.898	−0.464409
$161$	2253.65	1.10318
$162$	−2351.06	−1.14023
$163$	−2816.70	−1.35350	−0.676750	−	0.736212i	$-0.736612\pi$
$163$	−2816.70	−1.35350	−0.676750	+	0.736212i	$0.736612\pi$
$164$	−944.870	−0.449890
$165$	59.9867	0.0283028
$166$	−3843.76	−1.79719
$167$	−1898.52	−0.879712	−0.439856	−	0.898068i	$-0.644971\pi$
$167$	−1898.52	−0.879712	−0.439856	+	0.898068i	$0.644971\pi$
$168$	−81.2612	−0.0373181
$169$	−248.611	−0.113159
$170$	−2.88564	−0.00130187
$171$	2541.93	1.13676
$172$	625.431	0.277260
$173$	−3232.44	−1.42057	−0.710283	−	0.703916i	$-0.751433\pi$
$173$	−3232.44	−1.42057	−0.710283	+	0.703916i	$0.751433\pi$
$174$	23.4237	0.0102055
$175$	−882.618	−0.381255
$176$	−1905.11	−0.815925
$177$	87.1584	0.0370126
$178$	−2161.10	−0.910006
$179$	−1366.73	−0.570694	−0.285347	−	0.958424i	$-0.592109\pi$
$179$	−1366.73	−0.570694	−0.285347	+	0.958424i	$0.592109\pi$
$180$	579.910	0.240133
$181$	2031.77	0.834368	0.417184	−	0.908822i	$-0.363017\pi$
$181$	2031.77	0.834368	0.417184	+	0.908822i	$0.363017\pi$
$182$	−2235.99	−0.910675
$183$	159.334	0.0643622
$184$	2544.62	1.01952
$185$	3406.06	1.35361
$186$	−251.034	−0.0989608
$187$	−2.61720	−0.00102347
$188$	−163.181	−0.0633042
$189$	249.472	0.0960126
$190$	−2541.57	−0.970448
$191$	211.108	0.0799750	0.0399875	−	0.999200i	$-0.487268\pi$
$191$	211.108	0.0799750	0.0399875	+	0.999200i	$0.487268\pi$
$192$	−75.5583	−0.0284008
$193$	4031.89	1.50374	0.751871	−	0.659311i	$-0.229152\pi$
$193$	4031.89	1.50374	0.751871	+	0.659311i	$0.229152\pi$
$194$	1097.47	0.406153
$195$	108.498	0.0398446
$196$	−263.737	−0.0961140
$197$	197.000	0.0712470
$197$	197.000	0.0712470
$198$	2139.11	0.767778
$199$	−1075.38	−0.383075	−0.191537	−	0.981485i	$-0.561347\pi$
$199$	−1075.38	−0.383075	−0.191537	+	0.981485i	$0.561347\pi$
$200$	−996.572	−0.352341
$201$	−168.475	−0.0591209
$202$	5709.69	1.98877
$203$	375.930	0.129976
$204$	0.0832279	2.85643e−5 0
$205$	2992.62	1.01958
$206$	6021.09	2.03645
$207$	−3899.57	−1.30937
$208$	−3445.76	−1.14866
$209$	−2305.14	−0.762919
$210$	−124.513	−0.0409154
$211$	−2851.30	−0.930292	−0.465146	−	0.885234i	$-0.653998\pi$
$211$	−2851.30	−0.930292	−0.465146	+	0.885234i	$0.653998\pi$
$212$	−1351.33	−0.437781
$213$	−123.150	−0.0396155
$214$	1803.06	0.575955
$215$	−1980.89	−0.628350
$216$	281.680	0.0887312
$217$	−4028.87	−1.26036
$218$	2024.13	0.628859
$219$	100.209	0.0309201
$220$	−525.890	−0.161161
$221$	−4.73372	−0.00144084
$222$	−399.537	−0.120789
$223$	1564.14	0.469697	0.234848	−	0.972032i	$-0.424541\pi$
$223$	1564.14	0.469697	0.234848	+	0.972032i	$0.424541\pi$
$224$	1769.45	0.527795
$225$	1527.22	0.452511
$226$	−4688.28	−1.37991
$227$	−3686.82	−1.07799	−0.538994	−	0.842310i	$-0.681195\pi$
$227$	−3686.82	−1.07799	−0.538994	+	0.842310i	$0.681195\pi$
$228$	73.3044	0.0212926
$229$	5061.92	1.46070	0.730352	−	0.683071i	$-0.239356\pi$
$229$	5061.92	1.46070	0.730352	+	0.683071i	$0.239356\pi$
$230$	3899.02	1.11780
$231$	−112.931	−0.0321657
$232$	424.466	0.120119
$233$	6768.75	1.90316	0.951578	−	0.307407i	$-0.0994614\pi$
$233$	6768.75	1.90316	0.951578	+	0.307407i	$0.0994614\pi$
$234$	3869.01	1.08088
$235$	516.832	0.143466
$236$	−764.098	−0.210757
$237$	−146.519	−0.0401581
$238$	5.43248	0.00147956
$239$	353.255	0.0956074	0.0478037	−	0.998857i	$-0.484778\pi$
$239$	353.255	0.0956074	0.0478037	+	0.998857i	$0.484778\pi$
$240$	−191.881	−0.0516077
$241$	−2126.72	−0.568439	−0.284219	−	0.958759i	$-0.591734\pi$
$241$	−2126.72	−0.568439	−0.284219	+	0.958759i	$0.591734\pi$
$242$	2395.29	0.636260
$243$	−647.858	−0.171029
$244$	−1396.84	−0.366490
$245$	835.316	0.217822
$246$	−351.040	−0.0909818
$247$	−4169.31	−1.07404
$248$	−4549.04	−1.16477
$249$	−351.127	−0.0893645
$250$	−4890.47	−1.23720
$251$	6107.73	1.53592	0.767962	−	0.640496i	$-0.221271\pi$
$251$	6107.73	1.53592	0.767962	+	0.640496i	$0.221271\pi$
$252$	−1091.73	−0.272908
$253$	3536.31	0.878759
$254$	5374.38	1.32763
$255$	−0.263602	−6.47349e−5 0
$256$	3626.85	0.885462
$257$	−2096.67	−0.508897	−0.254449	−	0.967086i	$-0.581894\pi$
$257$	−2096.67	−0.508897	−0.254449	+	0.967086i	$0.581894\pi$
$258$	232.362	0.0560706
$259$	−6412.22	−1.53836
$260$	−951.177	−0.226883
$261$	−650.485	−0.154268
$262$	−1258.24	−0.296696
$263$	7932.84	1.85992	0.929962	−	0.367655i	$-0.119839\pi$
$263$	7932.84	1.85992	0.929962	+	0.367655i	$0.119839\pi$
$264$	−127.511	−0.0297263
$265$	4279.97	0.992138
$266$	4784.75	1.10290
$267$	−197.416	−0.0452496
$268$	1476.98	0.336645
$269$	736.004	0.166821	0.0834107	−	0.996515i	$-0.473419\pi$
$269$	736.004	0.166821	0.0834107	+	0.996515i	$0.473419\pi$
$270$	431.608	0.0972846
$271$	4856.77	1.08866	0.544332	−	0.838870i	$-0.316783\pi$
$271$	4856.77	1.08866	0.544332	+	0.838870i	$0.316783\pi$
$272$	8.37168	0.00186621
$273$	−204.257	−0.0452829
$274$	2696.19	0.594463
$275$	−1384.96	−0.303695
$276$	−112.456	−0.0245256
$277$	−6677.85	−1.44849	−0.724247	−	0.689540i	$-0.757813\pi$
$277$	−6677.85	−1.44849	−0.724247	+	0.689540i	$0.757813\pi$
$278$	1994.68	0.430335
$279$	6971.29	1.49592
$280$	−2256.33	−0.481577
$281$	−5626.19	−1.19441	−0.597207	−	0.802087i	$-0.703723\pi$
$281$	−5626.19	−1.19441	−0.597207	+	0.802087i	$0.703723\pi$
$282$	−60.6254	−0.0128021
$283$	−5348.60	−1.12347	−0.561733	−	0.827318i	$-0.689865\pi$
$283$	−5348.60	−1.12347	−0.561733	+	0.827318i	$0.689865\pi$
$284$	1079.63	0.225578
$285$	−232.172	−0.0482551
$286$	−3508.60	−0.725412
$287$	−5633.89	−1.15874
$288$	−3061.73	−0.626438
$289$	−4912.99	−0.999998
$290$	650.393	0.131698
$291$	100.254	0.0201958
$292$	−878.510	−0.176065
$293$	−5889.11	−1.17422	−0.587108	−	0.809509i	$-0.699734\pi$
$293$	−5889.11	−1.17422	−0.587108	+	0.809509i	$0.699734\pi$
$294$	−97.9842	−0.0194373
$295$	2420.08	0.477635
$296$	−7240.09	−1.42169
$297$	391.458	0.0764804
$298$	−1134.45	−0.220526
$299$	6396.13	1.23712
$300$	44.0422	0.00847592
$301$	3729.20	0.714112
$302$	5358.36	1.02099
$303$	521.578	0.0988908
$304$	7373.51	1.39112
$305$	4424.12	0.830572
$306$	−9.39999	−0.00175608
$307$	−860.391	−0.159951	−0.0799757	−	0.996797i	$-0.525484\pi$
$307$	−860.391	−0.159951	−0.0799757	+	0.996797i	$0.525484\pi$
$308$	990.036	0.183158
$309$	550.025	0.101262
$310$	−6970.31	−1.27705
$311$	−4317.20	−0.787158	−0.393579	−	0.919291i	$-0.628763\pi$
$311$	−4317.20	−0.787158	−0.393579	+	0.919291i	$0.628763\pi$
$312$	−230.629	−0.0418486
$313$	−2958.58	−0.534277	−0.267138	−	0.963658i	$-0.586078\pi$
$313$	−2958.58	−0.534277	−0.267138	+	0.963658i	$0.586078\pi$
$314$	−11730.5	−2.10825
$315$	3457.78	0.618488
$316$	1284.50	0.228667
$317$	7104.45	1.25876	0.629378	−	0.777099i	$-0.283310\pi$
$317$	7104.45	1.25876	0.629378	+	0.777099i	$0.283310\pi$
$318$	−502.049	−0.0885331
$319$	589.890	0.103534
$320$	−2097.98	−0.366502
$321$	164.709	0.0286391
$322$	−7340.27	−1.27036
$323$	10.1296	0.00174497
$324$	1882.83	0.322845
$325$	−2504.97	−0.427541
$326$	9174.12	1.55861
$327$	184.904	0.0312697
$328$	−6361.27	−1.07086
$329$	−972.984	−0.163047
$330$	−195.380	−0.0325918
$331$	3426.72	0.569031	0.284516	−	0.958671i	$-0.408167\pi$
$331$	3426.72	0.569031	0.284516	+	0.958671i	$0.408167\pi$
$332$	3078.25	0.508858
$333$	11095.3	1.82588
$334$	6183.58	1.01303
$335$	−4677.94	−0.762935
$336$	361.233	0.0586514
$337$	5875.10	0.949665	0.474833	−	0.880076i	$-0.342509\pi$
$337$	5875.10	0.949665	0.474833	+	0.880076i	$0.342509\pi$
$338$	809.740	0.130308
$339$	−428.273	−0.0686154
$340$	2.31094	0.000368613 0
$341$	−6321.90	−1.00396
$342$	−8279.21	−1.30903
$343$	−6907.16	−1.08732
$344$	4210.67	0.659954
$345$	356.175	0.0555820
$346$	10528.2	1.63584
$347$	4979.84	0.770408	0.385204	−	0.922831i	$-0.374131\pi$
$347$	4979.84	0.770408	0.385204	+	0.922831i	$0.374131\pi$
$348$	−18.7587	−0.00288958
$349$	5281.46	0.810057	0.405028	−	0.914304i	$-0.367262\pi$
$349$	5281.46	0.810057	0.405028	+	0.914304i	$0.367262\pi$
$350$	2874.73	0.439031
$351$	708.029	0.107669
$352$	2776.52	0.420423
$353$	−2372.59	−0.357734	−0.178867	−	0.983873i	$-0.557243\pi$
$353$	−2372.59	−0.357734	−0.178867	+	0.983873i	$0.557243\pi$
$354$	−283.880	−0.0426215
$355$	−3419.43	−0.511225
$356$	1730.70	0.257659
$357$	0.496255	7.35703e−5 0
$358$	4451.51	0.657178
$359$	8710.91	1.28062	0.640312	−	0.768115i	$-0.278805\pi$
$359$	8710.91	1.28062	0.640312	+	0.768115i	$0.278805\pi$
$360$	3904.21	0.571582
$361$	2062.81	0.300745
$362$	−6617.60	−0.960810
$363$	218.809	0.0316377
$364$	1790.68	0.257849
$365$	2782.45	0.399013
$366$	−518.958	−0.0741157
$367$	4737.76	0.673867	0.336934	−	0.941528i	$-0.390610\pi$
$367$	4737.76	0.673867	0.336934	+	0.941528i	$0.390610\pi$
$368$	−11311.7	−1.60234
$369$	9748.50	1.37530
$370$	−11093.7	−1.55874
$371$	−8057.44	−1.12755
$372$	201.039	0.0280198
$373$	6914.00	0.959767	0.479884	−	0.877332i	$-0.340679\pi$
$373$	6914.00	0.959767	0.479884	+	0.877332i	$0.340679\pi$
$374$	8.52435	0.00117857
$375$	−446.743	−0.0615192
$376$	−1098.60	−0.150681
$377$	1066.93	0.145756
$378$	−812.542	−0.110563
$379$	−2277.50	−0.308673	−0.154337	−	0.988018i	$-0.549324\pi$
$379$	−2277.50	−0.308673	−0.154337	+	0.988018i	$0.549324\pi$
$380$	2035.40	0.274773
$381$	490.948	0.0660158
$382$	−687.589	−0.0920945
$383$	1882.94	0.251211	0.125606	−	0.992080i	$-0.459913\pi$
$383$	1882.94	0.251211	0.125606	+	0.992080i	$0.459913\pi$
$384$	516.899	0.0686924
$385$	−3135.68	−0.415088
$386$	−13132.1	−1.73162
$387$	−6452.76	−0.847577
$388$	−878.900	−0.114998
$389$	4471.16	0.582768	0.291384	−	0.956606i	$-0.405884\pi$
$389$	4471.16	0.582768	0.291384	+	0.956606i	$0.405884\pi$
$390$	−353.383	−0.0458827
$391$	−15.5398	−0.00200992
$392$	−1775.59	−0.228778
$393$	−114.940	−0.0147531
$394$	−641.639	−0.0820439
$395$	−4068.32	−0.518226
$396$	−1713.09	−0.217389
$397$	−6932.41	−0.876392	−0.438196	−	0.898879i	$-0.644382\pi$
$397$	−6932.41	−0.876392	−0.438196	+	0.898879i	$0.644382\pi$
$398$	3502.58	0.441127
$399$	437.086	0.0548412
$400$	4430.09	0.553761
$401$	12031.6	1.49833	0.749163	−	0.662386i	$-0.230456\pi$
$401$	12031.6	1.49833	0.749163	+	0.662386i	$0.230456\pi$
$402$	548.731	0.0680801
$403$	−11434.4	−1.41337
$404$	−4572.56	−0.563102
$405$	−5963.36	−0.731659
$406$	−1224.42	−0.149673
$407$	−10061.7	−1.22541
$408$	0.560326	6.79909e−5 0
$409$	582.097	0.0703737	0.0351868	−	0.999381i	$-0.488797\pi$
$409$	582.097	0.0703737	0.0351868	+	0.999381i	$0.488797\pi$
$410$	−9747.13	−1.17409
$411$	246.296	0.0295594
$412$	−4821.94	−0.576602
$413$	−4556.02	−0.542825
$414$	12701.1	1.50779
$415$	−9749.53	−1.15322
$416$	5021.89	0.591871
$417$	182.214	0.0213982
$418$	7507.97	0.878533
$419$	3174.96	0.370184	0.185092	−	0.982721i	$-0.440742\pi$
$419$	3174.96	0.370184	0.185092	+	0.982721i	$0.440742\pi$
$420$	99.7156	0.0115848
$421$	3185.72	0.368794	0.184397	−	0.982852i	$-0.440967\pi$
$421$	3185.72	0.368794	0.184397	+	0.982852i	$0.440967\pi$
$422$	9286.84	1.07127
$423$	1683.59	0.193519
$424$	−9097.73	−1.04204
$425$	6.08598	0.000694619 0
$426$	401.106	0.0456189
$427$	−8328.81	−0.943933
$428$	−1443.96	−0.163076
$429$	−320.510	−0.0360708
$430$	6451.85	0.723572
$431$	5525.11	0.617483	0.308741	−	0.951146i	$-0.400092\pi$
$431$	5525.11	0.617483	0.308741	+	0.951146i	$0.400092\pi$
$432$	−1252.16	−0.139455
$433$	13661.7	1.51626	0.758130	−	0.652104i	$-0.226113\pi$
$433$	13661.7	1.51626	0.758130	+	0.652104i	$0.226113\pi$
$434$	13122.3	1.45136
$435$	59.4132	0.00654861
$436$	−1621.01	−0.178056
$437$	−13686.9	−1.49825
$438$	−326.386	−0.0356058
$439$	17008.5	1.84913	0.924567	−	0.381018i	$-0.124427\pi$
$439$	17008.5	1.84913	0.924567	+	0.381018i	$0.124427\pi$
$440$	−3540.52	−0.383608
$441$	2721.05	0.293818
$442$	15.4180	0.00165918
$443$	−13969.8	−1.49825	−0.749123	−	0.662430i	$-0.769525\pi$
$443$	−13969.8	−1.49825	−0.749123	+	0.662430i	$0.769525\pi$
$444$	319.966	0.0342003
$445$	−5481.52	−0.583930
$446$	−5094.48	−0.540876
$447$	−103.632	−0.0109656
$448$	3949.65	0.416525
$449$	−14558.2	−1.53016	−0.765082	−	0.643933i	$-0.777302\pi$
$449$	−14558.2	−1.53016	−0.765082	+	0.643933i	$0.777302\pi$
$450$	−4974.25	−0.521085
$451$	−8840.40	−0.923012
$452$	3754.57	0.390709
$453$	489.485	0.0507682
$454$	12008.2	1.24135
$455$	−5671.49	−0.584360
$456$	493.517	0.0506821
$457$	−2504.82	−0.256390	−0.128195	−	0.991749i	$-0.540918\pi$
$457$	−2504.82	−0.256390	−0.128195	+	0.991749i	$0.540918\pi$
$458$	−16486.9	−1.68206
$459$	−1.72020	−0.000174928 0
$460$	−3122.50	−0.316494
$461$	−10815.7	−1.09271	−0.546354	−	0.837554i	$-0.683985\pi$
$461$	−10815.7	−1.09271	−0.546354	+	0.837554i	$0.683985\pi$
$462$	367.821	0.0370402
$463$	5724.41	0.574592	0.287296	−	0.957842i	$-0.407244\pi$
$463$	5724.41	0.574592	0.287296	+	0.957842i	$0.407244\pi$
$464$	−1886.89	−0.188786
$465$	−636.736	−0.0635009
$466$	−22046.2	−2.19156
$467$	−12776.2	−1.26597	−0.632987	−	0.774162i	$-0.718171\pi$
$467$	−12776.2	−1.26597	−0.632987	+	0.774162i	$0.718171\pi$
$468$	−3098.47	−0.306040
$469$	8806.65	0.867065
$470$	−1683.35	−0.165207
$471$	−1071.58	−0.104832
$472$	−5144.24	−0.501658
$473$	5851.66	0.568837
$474$	477.221	0.0462437
$475$	5360.33	0.517787
$476$	−4.35056	−0.000418923 0
$477$	13942.1	1.33829
$478$	−1150.57	−0.110096
$479$	890.206	0.0849155	0.0424578	−	0.999098i	$-0.486481\pi$
$479$	890.206	0.0849155	0.0424578	+	0.999098i	$0.486481\pi$
$480$	279.649	0.0265920
$481$	−18198.6	−1.72512
$482$	6926.82	0.654581
$483$	−670.531	−0.0631682
$484$	−1918.25	−0.180151
$485$	2783.68	0.260619
$486$	2110.11	0.196947
$487$	8592.42	0.799507	0.399753	−	0.916623i	$-0.369096\pi$
$487$	8592.42	0.799507	0.399753	+	0.916623i	$0.369096\pi$
$488$	−9404.13	−0.872346
$489$	838.054	0.0775012
$490$	−2720.67	−0.250831
$491$	−14000.1	−1.28680	−0.643398	−	0.765532i	$-0.722476\pi$
$491$	−14000.1	−1.28680	−0.643398	+	0.765532i	$0.722476\pi$
$492$	281.128	0.0257606
$493$	−2.59218	−0.000236807 0
$494$	13579.7	1.23680
$495$	5425.76	0.492666
$496$	20222.0	1.83063
$497$	6437.40	0.581000
$498$	1143.64	0.102907
$499$	6167.22	0.553272	0.276636	−	0.960975i	$-0.410780\pi$
$499$	6167.22	0.553272	0.276636	+	0.960975i	$0.410780\pi$
$500$	3916.49	0.350302
$501$	564.869	0.0503722
$502$	−19893.2	−1.76868
$503$	6449.42	0.571701	0.285850	−	0.958274i	$-0.407724\pi$
$503$	6449.42	0.571701	0.285850	+	0.958274i	$0.407724\pi$
$504$	−7350.03	−0.649596
$505$	14482.4	1.27615
$506$	−11518.0	−1.01193
$507$	73.9695	0.00647949
$508$	−4304.03	−0.375906
$509$	−1949.07	−0.169727	−0.0848633	−	0.996393i	$-0.527045\pi$
$509$	−1949.07	−0.169727	−0.0848633	+	0.996393i	$0.527045\pi$
$510$	0.858566	7.45450e−5 0
$511$	−5238.21	−0.453473
$512$	2085.52	0.180015
$513$	−1515.09	−0.130396
$514$	6828.96	0.586016
$515$	15272.2	1.30675
$516$	−186.085	−0.0158759
$517$	−1526.75	−0.129877
$518$	20884.9	1.77149
$519$	961.751	0.0813414
$520$	−6403.73	−0.540042
$521$	13798.7	1.16033	0.580163	−	0.814500i	$-0.302989\pi$
$521$	13798.7	1.16033	0.580163	+	0.814500i	$0.302989\pi$
$522$	2118.66	0.177646
$523$	21367.6	1.78650	0.893250	−	0.449561i	$-0.148419\pi$
$523$	21367.6	1.78650	0.893250	+	0.449561i	$0.148419\pi$
$524$	1007.65	0.0840068
$525$	262.606	0.0218306
$526$	−25837.7	−2.14178
$527$	27.7806	0.00229628
$528$	566.828	0.0467197
$529$	8830.06	0.725739
$530$	−13940.1	−1.14249
$531$	7883.42	0.644278
$532$	−3831.83	−0.312276
$533$	−15989.6	−1.29941
$534$	642.993	0.0521068
$535$	4573.37	0.369578
$536$	9943.66	0.801307
$537$	406.645	0.0326779
$538$	−2397.20	−0.192102
$539$	−2467.58	−0.197191
$540$	−345.650	−0.0275452
$541$	−18713.8	−1.48719	−0.743595	−	0.668630i	$-0.766881\pi$
$541$	−18713.8	−1.48719	−0.743595	+	0.668630i	$0.766881\pi$
$542$	−15818.8	−1.25364
$543$	−604.516	−0.0477758
$544$	−12.2010	−0.000961604 0
$545$	5134.11	0.403525
$546$	665.277	0.0521451
$547$	−12519.0	−0.978561	−0.489280	−	0.872127i	$-0.662740\pi$
$547$	−12519.0	−0.978561	−0.489280	+	0.872127i	$0.662740\pi$
$548$	−2159.22	−0.168317
$549$	14411.6	1.12035
$550$	4510.88	0.349717
$551$	−2283.11	−0.176522
$552$	−757.103	−0.0583776
$553$	7658.98	0.588957
$554$	21750.1	1.66800
$555$	−1013.41	−0.0775076
$556$	−1597.43	−0.121845
$557$	−1180.39	−0.0897931	−0.0448965	−	0.998992i	$-0.514296\pi$
$557$	−1180.39	−0.0897931	−0.0448965	+	0.998992i	$0.514296\pi$
$558$	−22705.9	−1.72261
$559$	10583.9	0.800807
$560$	10030.1	0.756876
$561$	0.778698	5.86036e−5 0
$562$	18324.8	1.37542
$563$	−15586.9	−1.16680	−0.583401	−	0.812184i	$-0.698279\pi$
$563$	−15586.9	−1.16680	−0.583401	+	0.812184i	$0.698279\pi$
$564$	48.5514	0.00362479
$565$	−11891.6	−0.885458
$566$	17420.7	1.29372
$567$	11226.6	0.831520
$568$	7268.52	0.536937
$569$	−2743.60	−0.202140	−0.101070	−	0.994879i	$-0.532227\pi$
$569$	−2743.60	−0.202140	−0.101070	+	0.994879i	$0.532227\pi$
$570$	756.197	0.0555677
$571$	1194.38	0.0875360	0.0437680	−	0.999042i	$-0.486064\pi$
$571$	1194.38	0.0875360	0.0437680	+	0.999042i	$0.486064\pi$
$572$	2809.84	0.205394
$573$	−62.8111	−0.00457936
$574$	18349.9	1.33434
$575$	−8223.27	−0.596407
$576$	−6834.20	−0.494372
$577$	20968.2	1.51285	0.756427	−	0.654078i	$-0.226943\pi$
$577$	20968.2	1.51285	0.756427	+	0.654078i	$0.226943\pi$
$578$	16001.9	1.15154
$579$	−1199.61	−0.0861040
$580$	−520.862	−0.0372890
$581$	18354.4	1.31062
$582$	−326.531	−0.0232563
$583$	−12643.3	−0.898169
$584$	−5914.51	−0.419082
$585$	9813.57	0.693575
$586$	19181.1	1.35216
$587$	−3915.64	−0.275325	−0.137663	−	0.990479i	$-0.543959\pi$
$587$	−3915.64	−0.275325	−0.137663	+	0.990479i	$0.543959\pi$
$588$	78.4699	0.00550347
$589$	24468.2	1.71171
$590$	−7882.31	−0.550016
$591$	−58.6136	−0.00407959
$592$	32184.6	2.23442
$593$	−6327.58	−0.438183	−0.219091	−	0.975704i	$-0.570309\pi$
$593$	−6327.58	−0.438183	−0.219091	+	0.975704i	$0.570309\pi$
$594$	−1275.00	−0.0880704
$595$	13.7792	0.000949400 0
$596$	908.515	0.0624400
$597$	319.960	0.0219348
$598$	−20832.5	−1.42459
$599$	−1631.72	−0.111303	−0.0556513	−	0.998450i	$-0.517724\pi$
$599$	−1631.72	−0.111303	−0.0556513	+	0.998450i	$0.517724\pi$
$600$	296.511	0.0201750
$601$	1445.94	0.0981384	0.0490692	−	0.998795i	$-0.484375\pi$
$601$	1445.94	0.0981384	0.0490692	+	0.998795i	$0.484375\pi$
$602$	−12146.2	−0.822329
$603$	−15238.4	−1.02912
$604$	−4291.20	−0.289084
$605$	6075.54	0.408274
$606$	−1698.81	−0.113877
$607$	11038.7	0.738131	0.369065	−	0.929403i	$-0.379678\pi$
$607$	11038.7	0.738131	0.369065	+	0.929403i	$0.379678\pi$
$608$	−10746.2	−0.716804
$609$	−111.851	−0.00744241
$610$	−14409.6	−0.956438
$611$	−2761.44	−0.182841
$612$	7.52791	0.000497219 0
$613$	20856.3	1.37419	0.687096	−	0.726567i	$-0.258885\pi$
$613$	20856.3	1.37419	0.687096	+	0.726567i	$0.258885\pi$
$614$	2802.34	0.184191
$615$	−890.398	−0.0583810
$616$	6665.35	0.435965
$617$	5712.03	0.372703	0.186351	−	0.982483i	$-0.440334\pi$
$617$	5712.03	0.372703	0.186351	+	0.982483i	$0.440334\pi$
$618$	−1791.46	−0.116607
$619$	−25250.3	−1.63957	−0.819787	−	0.572669i	$-0.805908\pi$
$619$	−25250.3	−1.63957	−0.819787	+	0.572669i	$0.805908\pi$
$620$	5582.12	0.361586
$621$	2324.30	0.150195
$622$	14061.3	0.906445
$623$	10319.5	0.663629
$624$	1025.22	0.0657719
$625$	−5310.71	−0.339885
$626$	9636.24	0.615242
$627$	685.851	0.0436846
$628$	9394.30	0.596932
$629$	44.2146	0.00280278
$630$	−11262.2	−0.712215
$631$	−16775.7	−1.05837	−0.529183	−	0.848508i	$-0.677501\pi$
$631$	−16775.7	−1.05837	−0.529183	+	0.848508i	$0.677501\pi$
$632$	8647.82	0.544291
$633$	848.350	0.0532684
$634$	−23139.6	−1.44951
$635$	13631.9	0.851912
$636$	402.062	0.0250673
$637$	−4463.10	−0.277605
$638$	−1921.30	−0.119224
$639$	−11138.8	−0.689587
$640$	14352.4	0.886452
$641$	9988.54	0.615482	0.307741	−	0.951470i	$-0.400427\pi$
$641$	9988.54	0.615482	0.307741	+	0.951470i	$0.400427\pi$
$642$	−536.465	−0.0329791
$643$	26304.1	1.61327	0.806634	−	0.591051i	$-0.201287\pi$
$643$	26304.1	1.61327	0.806634	+	0.591051i	$0.201287\pi$
$644$	5878.40	0.359691
$645$	589.375	0.0359792
$646$	−32.9926	−0.00200941
$647$	7956.48	0.483464	0.241732	−	0.970343i	$-0.422284\pi$
$647$	7956.48	0.483464	0.241732	+	0.970343i	$0.422284\pi$
$648$	12676.0	0.768458
$649$	−7149.06	−0.432396
$650$	8158.82	0.492331
$651$	1198.71	0.0721679
$652$	−7347.03	−0.441306
$653$	2872.28	0.172130	0.0860652	−	0.996290i	$-0.472571\pi$
$653$	2872.28	0.172130	0.0860652	+	0.996290i	$0.472571\pi$
$654$	−602.241	−0.0360084
$655$	−3191.47	−0.190384
$656$	28278.0	1.68303
$657$	9063.85	0.538226
$658$	3169.06	0.187755
$659$	−15107.1	−0.893004	−0.446502	−	0.894783i	$-0.647330\pi$
$659$	−15107.1	−0.893004	−0.446502	+	0.894783i	$0.647330\pi$
$660$	156.469	0.00922807
$661$	−13750.5	−0.809127	−0.404563	−	0.914510i	$-0.632576\pi$
$661$	−13750.5	−0.809127	−0.404563	+	0.914510i	$0.632576\pi$
$662$	−11161.0	−0.655263
$663$	1.40843	8.25021e−5 0
$664$	20724.1	1.21122
$665$	12136.3	0.707707
$666$	−36137.9	−2.10257
$667$	3502.50	0.203325
$668$	−4952.07	−0.286829
$669$	−465.379	−0.0268948
$670$	15236.3	0.878551
$671$	−13069.1	−0.751905
$672$	−526.465	−0.0302215
$673$	3385.45	0.193907	0.0969535	−	0.995289i	$-0.469090\pi$
$673$	3385.45	0.193907	0.0969535	+	0.995289i	$0.469090\pi$
$674$	−19135.5	−1.09358
$675$	−910.287	−0.0519066
$676$	−648.474	−0.0368954
$677$	−20705.6	−1.17545	−0.587727	−	0.809059i	$-0.699977\pi$
$677$	−20705.6	−1.17545	−0.587727	+	0.809059i	$0.699977\pi$
$678$	1394.91	0.0790135
$679$	−5240.53	−0.296190
$680$	15.5582	0.000877399 0
$681$	1096.94	0.0617254
$682$	20590.7	1.15610
$683$	2748.19	0.153963	0.0769814	−	0.997033i	$-0.475472\pi$
$683$	2748.19	0.153963	0.0769814	+	0.997033i	$0.475472\pi$
$684$	6630.34	0.370639
$685$	6838.77	0.381454
$686$	22497.0	1.25210
$687$	−1506.08	−0.0836397
$688$	−18717.8	−1.03722
$689$	−22868.0	−1.26444
$690$	−1160.08	−0.0640050
$691$	−28050.7	−1.54428	−0.772142	−	0.635450i	$-0.780815\pi$
$691$	−28050.7	−1.54428	−0.772142	+	0.635450i	$0.780815\pi$
$692$	−8431.45	−0.463173
$693$	−10214.5	−0.559909
$694$	−16219.6	−0.887157
$695$	5059.42	0.276136
$696$	−126.292	−0.00687798
$697$	38.8477	0.00211114
$698$	−17202.0	−0.932814
$699$	−2013.91	−0.108974
$700$	−2302.21	−0.124308
$701$	−15551.0	−0.837877	−0.418939	−	0.908015i	$-0.637598\pi$
$701$	−15551.0	−0.837877	−0.418939	+	0.908015i	$0.637598\pi$
$702$	−2306.09	−0.123985
$703$	38942.8	2.08927
$704$	6197.57	0.331790
$705$	−153.773	−0.00821481
$706$	7727.64	0.411945
$707$	−27264.4	−1.45033
$708$	227.343	0.0120679
$709$	−4368.81	−0.231416	−0.115708	−	0.993283i	$-0.536914\pi$
$709$	−4368.81	−0.231416	−0.115708	+	0.993283i	$0.536914\pi$
$710$	11137.3	0.588696
$711$	−13252.6	−0.699031
$712$	11651.8	0.613300
$713$	−37536.6	−1.97161
$714$	−1.61633	−8.47193e−5 0
$715$	−8899.40	−0.465481
$716$	−3564.96	−0.186074
$717$	−105.104	−0.00547447
$718$	−28371.9	−1.47469
$719$	−8550.59	−0.443510	−0.221755	−	0.975102i	$-0.571178\pi$
$719$	−8550.59	−0.443510	−0.221755	+	0.975102i	$0.571178\pi$
$720$	−17355.5	−0.898334
$721$	−28751.4	−1.48510
$722$	−6718.68	−0.346320
$723$	632.763	0.0325487
$724$	5299.65	0.272044
$725$	−1371.72	−0.0702680
$726$	−712.672	−0.0364321
$727$	−16852.9	−0.859750	−0.429875	−	0.902888i	$-0.641442\pi$
$727$	−16852.9	−0.859750	−0.429875	+	0.902888i	$0.641442\pi$
$728$	12055.6	0.613751
$729$	−19296.9	−0.980382
$730$	−9062.57	−0.459480
$731$	−25.7142	−0.00130106
$732$	415.603	0.0209852
$733$	−18457.9	−0.930095	−0.465048	−	0.885286i	$-0.653963\pi$
$733$	−18457.9	−0.930095	−0.465048	+	0.885286i	$0.653963\pi$
$734$	−15431.1	−0.775986
$735$	−248.532	−0.0124725
$736$	16485.7	0.825642
$737$	13818.9	0.690674
$738$	−31751.4	−1.58372
$739$	11329.5	0.563955	0.281978	−	0.959421i	$-0.409010\pi$
$739$	11329.5	0.563955	0.281978	+	0.959421i	$0.409010\pi$
$740$	8884.31	0.441343
$741$	1240.50	0.0614991
$742$	26243.5	1.29842
$743$	−1810.71	−0.0894059	−0.0447029	−	0.999000i	$-0.514234\pi$
$743$	−1810.71	−0.0894059	−0.0447029	+	0.999000i	$0.514234\pi$
$744$	1353.48	0.0666948
$745$	−2877.48	−0.141507
$746$	−22519.2	−1.10521
$747$	−31759.2	−1.55557
$748$	−6.82666	−0.000333700 0
$749$	−8609.79	−0.420020
$750$	1455.07	0.0708420
$751$	11058.7	0.537332	0.268666	−	0.963233i	$-0.413417\pi$
$751$	11058.7	0.537332	0.268666	+	0.963233i	$0.413417\pi$
$752$	4883.66	0.236820
$753$	−1817.24	−0.0879467
$754$	−3475.06	−0.167844
$755$	13591.2	0.655147
$756$	650.718	0.0313047
$757$	−18384.6	−0.882692	−0.441346	−	0.897337i	$-0.645499\pi$
$757$	−18384.6	−0.882692	−0.441346	+	0.897337i	$0.645499\pi$
$758$	7417.92	0.355450
$759$	−1052.16	−0.0503176
$760$	13703.2	0.654035
$761$	−3179.76	−0.151467	−0.0757335	−	0.997128i	$-0.524130\pi$
$761$	−3179.76	−0.151467	−0.0757335	+	0.997128i	$0.524130\pi$
$762$	−1599.04	−0.0760200
$763$	−9665.43	−0.458600
$764$	550.650	0.0260757
$765$	−23.8426	−0.00112684
$766$	−6132.85	−0.289280
$767$	−12930.5	−0.608726
$768$	−1079.10	−0.0507014
$769$	2596.88	0.121776	0.0608881	−	0.998145i	$-0.480607\pi$
$769$	2596.88	0.121776	0.0608881	+	0.998145i	$0.480607\pi$
$770$	10213.1	0.477991
$771$	623.823	0.0291394
$772$	10516.7	0.490292
$773$	38095.1	1.77255	0.886277	−	0.463156i	$-0.153283\pi$
$773$	38095.1	1.77255	0.886277	+	0.463156i	$0.153283\pi$
$774$	21017.0	0.976020
$775$	14700.8	0.681379
$776$	−5917.13	−0.273728
$777$	1907.83	0.0880863
$778$	−14562.8	−0.671081
$779$	34215.8	1.57370
$780$	283.004	0.0129913
$781$	10101.2	0.462804
$782$	50.6138	0.00231451
$783$	387.715	0.0176958
$784$	7893.08	0.359561
$785$	−29753.9	−1.35282
$786$	374.366	0.0169888
$787$	2242.72	0.101581	0.0507905	−	0.998709i	$-0.483826\pi$
$787$	2242.72	0.101581	0.0507905	+	0.998709i	$0.483826\pi$
$788$	513.852	0.0232300
$789$	−2360.27	−0.106499
$790$	13250.7	0.596759
$791$	22387.1	1.00631
$792$	−11533.3	−0.517446
$793$	−23638.1	−1.05853
$794$	22579.2	1.00920
$795$	−1273.42	−0.0568097
$796$	−2805.01	−0.124901
$797$	16110.3	0.716006	0.358003	−	0.933720i	$-0.383458\pi$
$797$	16110.3	0.716006	0.358003	+	0.933720i	$0.383458\pi$
$798$	−1423.61	−0.0631519
$799$	6.70908	0.000297059 0
$800$	−6456.46	−0.285338
$801$	−17856.1	−0.787659
$802$	−39187.5	−1.72538
$803$	−8219.52	−0.361221
$804$	−439.447	−0.0192763
$805$	−18618.2	−0.815164
$806$	37242.5	1.62756
$807$	−218.984	−0.00955217
$808$	−30784.4	−1.34034
$809$	35408.8	1.53882	0.769412	−	0.638753i	$-0.220549\pi$
$809$	35408.8	1.53882	0.769412	+	0.638753i	$0.220549\pi$
$810$	19423.0	0.842535
$811$	−29961.3	−1.29727	−0.648633	−	0.761101i	$-0.724659\pi$
$811$	−29961.3	−1.29727	−0.648633	+	0.761101i	$0.724659\pi$
$812$	980.571	0.0423784
$813$	−1445.04	−0.0623367
$814$	32771.5	1.41111
$815$	23269.7	1.00013
$816$	−2.49083	−0.000106859 0
$817$	−22648.2	−0.969843
$818$	−1895.92	−0.0810382
$819$	−18474.9	−0.788238
$820$	7805.91	0.332432
$821$	41220.1	1.75224	0.876122	−	0.482090i	$-0.160122\pi$
$821$	41220.1	1.75224	0.876122	+	0.482090i	$0.160122\pi$
$822$	−802.200	−0.0340389
$823$	−6327.55	−0.268001	−0.134000	−	0.990981i	$-0.542782\pi$
$823$	−6327.55	−0.268001	−0.134000	+	0.990981i	$0.542782\pi$
$824$	−32463.4	−1.37247
$825$	412.068	0.0173895
$826$	14839.2	0.625086
$827$	−26605.5	−1.11870	−0.559350	−	0.828932i	$-0.688949\pi$
$827$	−26605.5	−1.11870	−0.559350	+	0.828932i	$0.688949\pi$
$828$	−10171.6	−0.426917
$829$	37088.6	1.55385	0.776925	−	0.629593i	$-0.216778\pi$
$829$	37088.6	1.55385	0.776925	+	0.629593i	$0.216778\pi$
$830$	31754.7	1.32798
$831$	1986.87	0.0829406
$832$	11209.5	0.467093
$833$	10.8434	0.000451021 0
$834$	−593.479	−0.0246409
$835$	15684.4	0.650036
$836$	−6012.70	−0.248748
$837$	−4155.17	−0.171594
$838$	−10341.0	−0.426282
$839$	11211.3	0.461333	0.230667	−	0.973033i	$-0.425909\pi$
$839$	11211.3	0.461333	0.230667	+	0.973033i	$0.425909\pi$
$840$	671.328	0.0275750
$841$	−23804.7	−0.976045
$842$	−10376.0	−0.424682
$843$	1673.96	0.0683919
$844$	−7437.29	−0.303320
$845$	2053.87	0.0836156
$846$	−5483.52	−0.222846
$847$	−11437.8	−0.463998
$848$	40442.4	1.63773
$849$	1591.37	0.0643295
$850$	−19.8223	−0.000799883 0
$851$	−59742.0	−2.40650
$852$	−321.223	−0.0129166
$853$	−36808.1	−1.47748	−0.738738	−	0.673993i	$-0.764578\pi$
$853$	−36808.1	−1.47748	−0.738738	+	0.673993i	$0.764578\pi$
$854$	27127.4	1.08698
$855$	−20999.8	−0.839975
$856$	−9721.38	−0.388166
$857$	−3442.46	−0.137214	−0.0686068	−	0.997644i	$-0.521855\pi$
$857$	−3442.46	−0.137214	−0.0686068	+	0.997644i	$0.521855\pi$
$858$	1043.92	0.0415370
$859$	−6614.42	−0.262725	−0.131363	−	0.991334i	$-0.541935\pi$
$859$	−6614.42	−0.262725	−0.131363	+	0.991334i	$0.541935\pi$
$860$	−5166.91	−0.204872
$861$	1676.26	0.0663492
$862$	−17995.6	−0.711057
$863$	−47138.8	−1.85935	−0.929677	−	0.368376i	$-0.879914\pi$
$863$	−47138.8	−1.85935	−0.929677	+	0.368376i	$0.879914\pi$
$864$	1824.91	0.0718575
$865$	26704.4	1.04968
$866$	−44496.9	−1.74604
$867$	1461.77	0.0572597
$868$	−10508.9	−0.410938
$869$	12018.1	0.469143
$870$	−193.512	−0.00754100
$871$	24994.3	0.972329
$872$	−10913.3	−0.423821
$873$	9067.87	0.351547
$874$	44579.0	1.72529
$875$	23352.5	0.902239
$876$	261.384	0.0100814
$877$	31400.3	1.20902	0.604510	−	0.796597i	$-0.293369\pi$
$877$	31400.3	1.20902	0.604510	+	0.796597i	$0.293369\pi$
$878$	−55397.5	−2.12936
$879$	1752.19	0.0672354
$880$	15738.8	0.602902
$881$	27904.8	1.06712	0.533562	−	0.845761i	$-0.320853\pi$
$881$	27904.8	1.06712	0.533562	+	0.845761i	$0.320853\pi$
$882$	−8862.60	−0.338344
$883$	27053.5	1.03106	0.515529	−	0.856872i	$-0.327596\pi$
$883$	27053.5	1.03106	0.515529	+	0.856872i	$0.327596\pi$
$884$	−12.3474	−0.000469782 0
$885$	−720.047	−0.0273493
$886$	45500.2	1.72529
$887$	38756.4	1.46709	0.733546	−	0.679639i	$-0.237864\pi$
$887$	38756.4	1.46709	0.733546	+	0.679639i	$0.237864\pi$
$888$	2154.15	0.0814060
$889$	−25663.2	−0.968186
$890$	17853.6	0.672420
$891$	17616.1	0.662360
$892$	4079.87	0.153144
$893$	5909.14	0.221435
$894$	337.534	0.0126273
$895$	11291.1	0.421697
$896$	−27019.8	−1.00744
$897$	−1903.05	−0.0708370
$898$	47416.8	1.76205
$899$	−6261.46	−0.232293
$900$	3983.59	0.147540
$901$	55.5590	0.00205432
$902$	28793.6	1.06289
$903$	−1109.55	−0.0408899
$904$	25277.4	0.929993
$905$	−16785.2	−0.616530
$906$	−1594.28	−0.0584617
$907$	−23050.6	−0.843861	−0.421930	−	0.906628i	$-0.638647\pi$
$907$	−23050.6	−0.843861	−0.421930	+	0.906628i	$0.638647\pi$
$908$	−9616.66	−0.351476
$909$	47176.4	1.72139
$910$	18472.3	0.672914
$911$	5461.95	0.198642	0.0993209	−	0.995055i	$-0.468333\pi$
$911$	5461.95	0.198642	0.0993209	+	0.995055i	$0.468333\pi$
$912$	−2193.85	−0.0796551
$913$	28800.7	1.04399
$914$	8158.32	0.295244
$915$	−1316.31	−0.0475584
$916$	13203.4	0.476260
$917$	6008.24	0.216368
$918$	5.60277	0.000201437 0
$919$	−16139.2	−0.579308	−0.289654	−	0.957131i	$-0.593540\pi$
$919$	−16139.2	−0.579308	−0.289654	+	0.957131i	$0.593540\pi$
$920$	−21022.0	−0.753343
$921$	255.993	0.00915879
$922$	35227.4	1.25830
$923$	18270.1	0.651535
$924$	−294.566	−0.0104876
$925$	23397.3	0.831673
$926$	−18644.7	−0.661666
$927$	49749.4	1.76266
$928$	2749.98	0.0972762
$929$	−44343.7	−1.56606	−0.783030	−	0.621983i	$-0.786327\pi$
$929$	−44343.7	−1.56606	−0.783030	+	0.621983i	$0.786327\pi$
$930$	2073.88	0.0731240
$931$	9550.49	0.336203
$932$	17655.5	0.620521
$933$	1284.50	0.0450725
$934$	41612.6	1.45782
$935$	21.6216	0.000756260 0
$936$	−20860.2	−0.728459
$937$	−6439.87	−0.224526	−0.112263	−	0.993679i	$-0.535810\pi$
$937$	−6439.87	−0.224526	−0.112263	+	0.993679i	$0.535810\pi$
$938$	−28683.7	−0.998461
$939$	880.268	0.0305926
$940$	1348.10	0.0467767
$941$	11377.8	0.394162	0.197081	−	0.980387i	$-0.436854\pi$
$941$	11377.8	0.394162	0.197081	+	0.980387i	$0.436854\pi$
$942$	3490.19	0.120718
$943$	−52490.4	−1.81264
$944$	22867.8	0.788437
$945$	−2060.98	−0.0709455
$946$	−19059.2	−0.655039
$947$	2029.00	0.0696236	0.0348118	−	0.999394i	$-0.488917\pi$
$947$	2029.00	0.0696236	0.0348118	+	0.999394i	$0.488917\pi$
$948$	−382.179	−0.0130935
$949$	−14866.6	−0.508526
$950$	−17458.9	−0.596253
$951$	−2113.79	−0.0720762
$952$	−29.2898	−0.000997152 0
$953$	−18497.6	−0.628747	−0.314373	−	0.949299i	$-0.601794\pi$
$953$	−18497.6	−0.628747	−0.314373	+	0.949299i	$0.601794\pi$
$954$	−45410.0	−1.54109
$955$	−1744.04	−0.0590950
$956$	921.426	0.0311726
$957$	−175.510	−0.00592837
$958$	−2899.45	−0.0977838
$959$	−12874.6	−0.433517
$960$	624.215	0.0209859
$961$	37313.5	1.25251
$962$	59273.8	1.98655
$963$	14897.8	0.498520
$964$	−5547.29	−0.185338
$965$	−33308.9	−1.11114
$966$	2183.96	0.0727408
$967$	−12880.3	−0.428339	−0.214170	−	0.976796i	$-0.568705\pi$
$967$	−12880.3	−0.428339	−0.214170	+	0.976796i	$0.568705\pi$
$968$	−12914.5	−0.428809
$969$	−3.01386	−9.99167e−5 0
$970$	−9066.59	−0.300114
$971$	11969.8	0.395600	0.197800	−	0.980242i	$-0.436620\pi$
$971$	11969.8	0.395600	0.197800	+	0.980242i	$0.436620\pi$
$972$	−1689.86	−0.0557638
$973$	−9524.82	−0.313825
$974$	−27986.0	−0.920665
$975$	745.307	0.0244809
$976$	41804.5	1.37103
$977$	−5543.99	−0.181544	−0.0907718	−	0.995872i	$-0.528933\pi$
$977$	−5543.99	−0.181544	−0.0907718	+	0.995872i	$0.528933\pi$
$978$	−2729.59	−0.0892459
$979$	16192.8	0.528624
$980$	2178.83	0.0710205
$981$	16724.4	0.544311
$982$	45599.2	1.48180
$983$	−47280.6	−1.53410	−0.767048	−	0.641590i	$-0.778275\pi$
$983$	−47280.6	−1.53410	−0.767048	+	0.641590i	$0.778275\pi$
$984$	1892.67	0.0613173
$985$	−1627.49	−0.0526458
$986$	8.44285	0.000272693 0
$987$	289.493	0.00933602
$988$	−10875.2	−0.350187
$989$	34744.6	1.11710
$990$	−17672.0	−0.567326
$991$	−19940.0	−0.639167	−0.319584	−	0.947558i	$-0.603543\pi$
$991$	−19940.0	−0.639167	−0.319584	+	0.947558i	$0.603543\pi$
$992$	−29471.7	−0.943274
$993$	−1019.55	−0.0325826
$994$	−20966.9	−0.669045
$995$	8884.13	0.283061
$996$	−915.874	−0.0291371
$997$	−11334.5	−0.360047	−0.180024	−	0.983662i	$-0.557617\pi$
$997$	−11334.5	−0.360047	−0.180024	+	0.983662i	$0.557617\pi$
$998$	−20087.0	−0.637116
$999$	−6613.23	−0.209443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.a.1.6	✓	22
3.2	odd	2		1773.4.a.c.1.17		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.a.1.6	✓	22	1.1	even	1	trivial
1773.4.a.c.1.17		22	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-3.25705 q^{2} -0.297531 q^{3} +2.60839 q^{4} -8.26136 q^{5} +0.969073 q^{6} +15.5528 q^{7} +17.5608 q^{8} -26.9115 q^{9} +26.9077 q^{10} +24.4046 q^{11} -0.776075 q^{12} +44.1406 q^{13} -50.6562 q^{14} +2.45801 q^{15} -78.0634 q^{16} -0.107242 q^{17} +87.6521 q^{18} -94.4553 q^{19} -21.5488 q^{20} -4.62743 q^{21} -79.4870 q^{22} +144.904 q^{23} -5.22487 q^{24} -56.7499 q^{25} -143.768 q^{26} +16.0403 q^{27} +40.5676 q^{28} +24.1713 q^{29} -8.00587 q^{30} -259.045 q^{31} +113.770 q^{32} -7.26112 q^{33} +0.349293 q^{34} -128.487 q^{35} -70.1955 q^{36} -412.288 q^{37} +307.646 q^{38} -13.1332 q^{39} -145.076 q^{40} -362.243 q^{41} +15.0718 q^{42} +239.777 q^{43} +63.6566 q^{44} +222.325 q^{45} -471.959 q^{46} -62.5601 q^{47} +23.2263 q^{48} -101.111 q^{49} +184.837 q^{50} +0.0319078 q^{51} +115.136 q^{52} -518.071 q^{53} -52.2442 q^{54} -201.615 q^{55} +273.119 q^{56} +28.1034 q^{57} -78.7271 q^{58} -292.939 q^{59} +6.41144 q^{60} -535.519 q^{61} +843.724 q^{62} -418.548 q^{63} +253.951 q^{64} -364.661 q^{65} +23.6498 q^{66} +566.243 q^{67} -0.279729 q^{68} -43.1133 q^{69} +418.489 q^{70} +413.907 q^{71} -472.586 q^{72} -336.802 q^{73} +1342.84 q^{74} +16.8848 q^{75} -246.376 q^{76} +379.559 q^{77} +42.7754 q^{78} +492.451 q^{79} +644.910 q^{80} +721.837 q^{81} +1179.85 q^{82} +1180.14 q^{83} -12.0701 q^{84} +0.885966 q^{85} -780.967 q^{86} -7.19170 q^{87} +428.563 q^{88} +663.513 q^{89} -724.125 q^{90} +686.508 q^{91} +377.964 q^{92} +77.0740 q^{93} +203.762 q^{94} +780.330 q^{95} -33.8502 q^{96} -336.952 q^{97} +329.324 q^{98} -656.764 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 6 q^{2} - 34 q^{3} + 68 q^{4} - 31 q^{5} - 24 q^{6} - 102 q^{7} - 93 q^{8} + 152 q^{9} - 133 q^{10} - 100 q^{11} - 272 q^{12} - 223 q^{13} - 55 q^{14} - 166 q^{15} + 112 q^{16} - 114 q^{17} - 389 q^{18}+ \cdots - 502 q^{99}+O(q^{100}) \) 22 * q - 6 * q^2 - 34 * q^3 + 68 * q^4 - 31 * q^5 - 24 * q^6 - 102 * q^7 - 93 * q^8 + 152 * q^9 - 133 * q^10 - 100 * q^11 - 272 * q^12 - 223 * q^13 - 55 * q^14 - 166 * q^15 + 112 * q^16 - 114 * q^17 - 389 * q^18 - 529 * q^19 - 441 * q^20 - 148 * q^21 - 671 * q^22 - 208 * q^23 - 555 * q^24 + 35 * q^25 - 408 * q^26 - 994 * q^27 - 1202 * q^28 - 2 * q^29 - 365 * q^30 - 1261 * q^31 - 1020 * q^32 - 790 * q^33 - 814 * q^34 - 968 * q^35 + 94 * q^36 - 792 * q^37 - 184 * q^38 - 368 * q^39 - 1914 * q^40 - 271 * q^41 - 1157 * q^42 - 1349 * q^43 - 998 * q^44 - 1533 * q^45 - 1371 * q^46 - 986 * q^47 - 1966 * q^48 - 40 * q^49 + 1631 * q^50 - 36 * q^51 - 1382 * q^52 + 248 * q^53 + 2903 * q^54 - 566 * q^55 + 4800 * q^56 + 914 * q^57 + 351 * q^58 - 1281 * q^59 + 5149 * q^60 + 510 * q^61 + 2237 * q^62 + 120 * q^63 + 3185 * q^64 + 2558 * q^65 + 8308 * q^66 - 3070 * q^67 + 4625 * q^68 + 302 * q^69 + 2087 * q^70 + 101 * q^71 + 4511 * q^72 - 3352 * q^73 + 4501 * q^74 - 752 * q^75 - 334 * q^76 - 492 * q^77 + 7825 * q^78 - 1313 * q^79 + 3098 * q^80 + 2078 * q^81 - 1243 * q^82 - 2631 * q^83 + 7518 * q^84 + 84 * q^85 + 7448 * q^86 - 1046 * q^87 - 3285 * q^88 + 798 * q^89 + 6009 * q^90 - 3992 * q^91 + 5966 * q^92 + 1978 * q^93 + 3517 * q^94 + 284 * q^95 + 10181 * q^96 - 3693 * q^97 + 2932 * q^98 - 502 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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